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FUTURE LOGIC

© Avi Sion, 1990 (Rev. ed. 1996) All rights reserved.

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APPENDIX 1:

On Factorial Analysis (Open Systems Analysis).

The table below is an appendix to Chapter 53 (in particular, Section 5).

It shows the factorial analysis of all 195 gross formulas (listed in the column labeled FORMULAS), in terms of the 63 factors (columns F1-F63) in the ‘open system’ of mixed (natural and temporal) modality.

Due to the size of the table, it is here split into three segments.

Thus, to see the factors allowed for by any gross formula, it is necessary to look along the row corresponding to it in all three segments.

The factors of any gross formula are signaled by a ‘1‘ in the cell concerned (where row and column cross); if a cell is blank, it means that the factor heading the column is not a possible outcome of the gross formula heading the row.

The gross formulas are first sorted into elements and compounds. Then the 20 elementary (plural) propositions and the remaining 175 compound formulas (consisting of two or more elements) are, respectively, sorted according to the number of factors they each have (indicated in the column labeled NF).

The factors of the 20 elements are already known (see ch. 52). The factors of the remaining 175 gross formulas (compounds), follow automatically from them. We need only do the following:

1. Split the compound into its component elements (which number two, three or four, as the case may be).

2. Look and see which, if any, of these elements have the factor concerned.

3. If all have it, the compound in question also has it; otherwise, not.

(For example, the compound AcInOp has factor F8, because its three component elements Ac, In and Op, have only this one factor F8 in common.)

The value of this table is, as we have seen (ch. 54-59), to guide us in generalization and particularization, by indicating successive inductive preferences. In some cases (the eleven cases with a single factor, to be specific), it even indicates deductive inferences.

APPENDIX TO CHAPTER 53 – FIRST SEGMENT – FACTORS F1-F21.

NF = Number of Factors.

NF

FORMULAS

F1F2F3F4F5F6F7F8F9F10F11F12F13F14F15F16F17F18F19F20F21
Elements:
1An100000000000000000000
1En010000000000000000000
3Ac101000010000000000000
3Ec010100001000000000000
7A101010010001000010000
7E010101001000100001000
15At101011010001010010101
15Et010111001000101001011
31Ap101111010101010111111
31Ep011111001010101111111
32In100000110101010000000
32On010000101010101000000
48Ic101000110111010110100
48Oc010100101110101101010
56I101010110111011110111
56O010101101110111101111
60It101011110111111111111
60Ot010111101111111111111
62Ip101111111111111111111
62Op011111111111111111111
Compounds:
1AcInOp000000010000000000000
1AcEp001000000000000000000
1AIcEpOt000000000000000010000
1AEt000010000000000000000
1AtIEtO000000000000000000001
1AtE000001000000000000000
1ApItEOc000000000000000001000
1ApEc000100000000000000000
1IpEcOn000000001000000000000
2AcIn100000010000000000000
2AcOp001000010000000000000
2AInOt000000000001000000000
2AIcEp001000000000000010000
2AEpOt000010000000000010000
2AtIcEpO000000000000000000100
2AtIEt000010000000000000001
2AtEtO000001000000000000001
2ApIEtOc000000000000000000010
2ApItE000001000000000001000
2ApEOc000100000000000001000
2ItEOn000000000000100000000
2IpEc000100001000000000000
2EcOn010000001000000000000
3AInOp000000010001000000000
3AIcOt000000000001000010000
3AEp001010000000000010000
3AtIcEpOt000000000000000010100
3AtIEpO000000000000000000101
3AtEt000011000000000000001
3ApIEtO000000000000000000011
3ApItEtOc000000000000000001010
3ApE000101000000000001000
3ItEOc000000000000100001000
3IpEOn000000001000100000000
4AIn100000010001000000000
4AOt000010000001000010000
4AtInO000000000000010000000
4AtIcEp001000000000000010100
4AtEpO000001000000000000101
4ApIcEpOc000000000000000100000
4ApIEt000010000000000000011
4ApEtOc000100000000000001010
4IEtOn000000000000001000000
4ItE000001000000100001000
4EOn010000001000100000000
5AIcOp001000010001000010000
5AtIEpOt000010000000000010101
5ApItEtO000001000000000001011
5IpEOc000100001000100001000
6AIc101000010001000010000
6AOp001010010001000010000
6AtInOt000000000001010000000
6AtIcO000000000000010000100
6AtIEp001010000000000010101
6AtEpOt000011000000000010101
6ApIcEpO000000000000000100100
6ApIEpOc000000000000000100010
6ApItEt000011000000000001011
6ApEtO000101000000000001011
6IEtOc000000000000001000010
6ItEtOn000000000000101000000
6IpE000101001000100001000
6EOc010100001000100001000
7AtInOp000000010001010000000
7AtIO000000000000010000101
7AtEp001011000000000010101
7ApIcEpOt000000000000000110100
7ApItEpOc000000000000000101010
7ApEt000111000000000001011
7IEtO000000000000001000011
7IpEtOn000000001000101000000
8AtIn100000010001010000000
8AtO000001000000010000101
8ApInOc000000000100000000000
8ApIcEp001000000000000110100
8ApEpOc000100000000000101010
8IcEpOn000000000010000000000
8IEt000010000000001000011
8EtOn010000001000101000000
9AtIcOt000000000001010010100
9ApIEpO000000000000000100111
9ItEtOc000000000000101001010
11AtIcOp001000010001010010100
11AtIOt000010000001010010101
11ApIEpOt000010000000000110111
11ApItEpO000001000000000101111
11ItEtO000001000000101001011
11IpEtOc000100001000101001010
12AtIc101000010001010010100
12AtOt000011000001010010101
12ApInO000000000100010000000
12ApIcOc000000000100000100000
12ApIEp001010000000000110111
12ApEpO000101000000000101111
12IcEpOc000000000010000100000
12IEpOn000000000010001000000
12ItEt000011000000101001011
12EtOc010100001000101001010
13AtIOp001010010001010010101
13ApItEpOt000011000000000111111
13IpEtO000101001000101001011
14AtI101010010001010010101
14AtOp001011010001010010101
14ApInOt000000000101010000000
14ApIOc000000000100000100010
14ApItEp001011000000000111111
14ApEpOt000111000000000111111
14IcEpO000000000010000100100
14ItEpOn000000000010101000000
14IpEt000111001000101001011
14EtO010101001000101001011
15ApInOp000000010101010000000
15ApItOc000000000100000101010
15ApEp001111000000000111111
15IcEpOt000000000010000110100
15IpEpOn000000001010101000000
16ApIn100000010101010000000
16ApOc000100000100000101010
16InOn000000100000000000000
16IcEp001000000010000110100
16EpOn010000001010101000000
18ApIcO000000000100010100100
18IEpOc000000000010001100010
21ApIcOt000000000101010110100
21ApIO000000000100010100111
21IEpO000000000010001100111
21ItEpOc000000000010101101010
23ApIcOp001000010101010110100
23ApItO000001000100010101111
23IEpOt000010000010001110111
23IpEpOc000100001010101101010
24ApIc101000010101010110100
24ApO000101000100010101111
24InOc000000100100000000000
24IcOn000000100010000000000
24IEp001010000010001110111
24EpOc010100001010101101010
25ApIOt000010000101010110111
25ItEpO000001000010101101111
27ApIOp001010010101010110111
27ApItOt000011000101010111111
27ItEpOt000011000010101111111
27IpEpO000101001010101101111
28ApI101010010101010110111
28ApOt000111000101010111111
28InO000000100100010000000
28IOn000000100010001000000
28ItEp001011000010101111111
28EpO010101001010101101111
29ApItOp001011010101010111111
29IpEpOt000111001010101111111
30ApIt101011010101010111111
30ApOp001111010101010111111
30InOt000000100101010000000
30ItOn000000100010101000000
30IpEp001111001010101111111
30EpOt010111001010101111111
31InOp000000110101010000000
31IpOn000000101010101000000
36IcOc000000100110000100000
42IcO000000100110010100100
42IOc000000100110001100010
45IcOt000000100111010110100
45ItOc000000100110101101010
47IcOp001000110111010110100
47IpOc000100101110101101010
49IO000000100110011100111
53IOt000010100111011110111
53ItO000001100110111101111
55IOp001010110111011110111
55IpO000101101110111101111
57ItOt000011100111111111111
59ItOp001011110111111111111
59IpOt000111101111111111111
61IpOp001111111111111111111

CONTINUED IN NEXT SEGMENT

APPENDIX TO CHAPTER 53 – SECOND SEGMENT – FACTORS F22-F42.

NF = Number of Factors.

NF

FORMULAS

F22F23F24F25F26F27F28F29F30F31F32F33F34F35F36F37F38F39F40F41F42
Elements:
1An000000000000000000000
1En000000000000000000000
3Ac000000000000000000000
3Ec000000000000000000000
7A000000100000000000000
7E000000010000000000000
15At000000101000001000100
15Et000000010100000100010
31Ap000010101010101011110
31Ep000001010101010111110
32In111110101010101000001
32On111101010101010100001
48Ic111111101011111011101
48Oc111111010111110111011
56I111111101111111111111
56O111111011111111111111
60It111111111111111111111
60Ot111111111111111111111
62Ip111111111111111111111
62Op111111111111111111111
Compounds:
1AcInOp000000000000000000000
1AcEp000000000000000000000
1AIcEpOt000000000000000000000
1AEt000000000000000000000
1AtIEtO000000000000000000000
1AtE000000000000000000000
1ApItEOc000000000000000000000
1ApEc000000000000000000000
1IpEcOn000000000000000000000
2AcIn000000000000000000000
2AcOp000000000000000000000
2AInOt000000100000000000000
2AIcEp000000000000000000000
2AEpOt000000000000000000000
2AtIcEpO000000000000000000100
2AtIEt000000000000000000000
2AtEtO000000000000000000000
2ApIEtOc000000000000000000010
2ApItE000000000000000000000
2ApEOc000000000000000000000
2ItEOn000000010000000000000
2IpEc000000000000000000000
2EcOn000000000000000000000
3AInOp000000100000000000000
3AIcOt000000100000000000000
3AEp000000000000000000000
3AtIcEpOt000000000000000000100
3AtIEpO000000000000000000100
3AtEt000000000000000000000
3ApIEtO000000000000000000010
3ApItEtOc000000000000000000010
3ApE000000000000000000000
3ItEOc000000010000000000000
3IpEOn000000010000000000000
4AIn000000100000000000000
4AOt000000100000000000000
4AtInO000000001000001000000
4AtIcEp000000000000000000100
4AtEpO00000000000000000 0 100
4ApIcEpOc000000000000000011000
4ApIEt000000000000000000010
4ApEtOc000000000000000000010
4IEtOn000000000100000100000
4ItE000000010000000000000
4EOn000000010000000000000
5AIcOp000000100000000000000
5AtIEpOt000000000000000000100
5ApItEtO000000000000000000010
5IpEOc000000010000000000000
6AIc000000100000000000000
6AOp000000100000000000000
6AtInOt000000101000001000000
6AtIcO000000001000001000100
6AtIEp000000000000000000100
6AtEpOt000000000000000000100
6ApIcEpO000000000000000011100
6ApIEpOc000000000000000011010
6ApItEt000000000000000000010
6ApEtO000000000000000000010
6IEtOc000000000100000100010
6ItEtOn000000010100000100000
6IpE000000010000000000000
6EOc000000010000000000000
7AtInOp000000101000001000000
7AtIO000000001000001000100
7AtEp000000000000000000100
7ApIcEpOt000000000000000011100
7ApItEpOc000000000000000011010
7ApEt000000000000000000010
7IEtO000000000100000100010
7IpEtOn000000010100000100000
8AtIn000000101000001000000
8AtO000000001000001000100
8ApInOc000010000010100000000
8ApIcEp000000000000000011100
8ApEpOc000000000000000011010
8IcEpOn000001000001010000000
8IEt000000000100000100010
8EtOn000000010100000100000
9AtIcOt000000101000001000100
9ApIEpO000000000000000011110
9ItEtOc000000010100000100010
11AtIcOp000000101000001000100
11AtIOt000000101000001000100
11ApIEpOt000000000000000011110
11ApItEpO000000000000000011110
11ItEtO000000010100000100010
11IpEtOc000000010100000100010
12AtIc000000101000001000100
12AtOt000000101000001000100
12ApInO000010001010101000000
12ApIcOc000010000010100011000
12ApIEp000000000000000011110
12ApEpO000000000000000011110
12IcEpOc000001000001010011000
12IEpOn000001000101010100000
12ItEt000000010100000100010
12EtOc000000010100000100010
13AtIOp000000101000001000100
13ApItEpOt000000000000000011110
13IpEtO000000010100000100010
14AtI000000101000001000100
14AtOp000000101000001000100
14ApInOt000010101010101000000
14ApIOc000010000010100011010
14ApItEp000000000000000011110
14ApEpOt000000000000000011110
14IcEpO000001000001010011100
14ItEpOn000001010101010100000
14IpEt000000010100000100010
14EtO000000010100000100010
15ApInOp000010101010101000000
15ApItOc000010000010100011010
15ApEp000000000000000011110
15IcEpOt000001000001010011100
15IpEpOn000001010101010100000
16ApIn000010101010101000000
16ApOc000010000010100011010
16InOn111100000000000000001
16IcEp000001000001010011100
16EpOn000001010101010100000
18ApIcO000010001010101011100
18IEpOc000001000101010111010
21ApIcOt000010101010101011100
21ApIO000010001010101011110
21IEpO000001000101010111110
21ItEpOc000001010101010111010
23ApIcOp000010101010101011100
23ApItO000010001010101011110
23IEpOt000001000101010111110
23IpEpOc000001010101010111010
24ApIc000010101010101011100
24ApO000010001010101011110
24InOc111110000010100000001
24IcOn111101000001010000001
24IEp000001000101010111110
24EpOc000001010101010111010
25ApIOt000010101010101011110
25ItEpO000001010101010111110
27ApIOp000010101010101011110
27ApItOt000010101010101011110
27ItEpOt000001010101010111110
27IpEpO000001010101010111110
28ApI000010101010101011110
28ApOt000010101010101011110
28InO111110001010101000001
28IOn111101000101010100001
28ItEp000001010101010111110
28EpO000001010101010111110
29ApItOp000010101010101011110
29IpEpOt000001010101010111110
30ApIt000010101010101011110
30ApOp000010101010101011110
30InOt111110101010101000001
30ItOn111101010101010100001
30IpEp000001010101010111110
30EpOt000001010101010111110
31InOp111110101010101000001
31IpOn111101010101010100001
36IcOc111111000011110011001
42IcO111111001011111011101
42IOc111111000111110111011
45IcOt111111101011111011101
45ItOc111111010111110111011
47IcOp111111101011111011101
47IpOc111111010111110111011
49IO111111001111111111111
53IOt111111101111111111111
53ItO111111011111111111111
55IOp111111101111111111111
55IpO111111011111111111111
57ItOt111111111111111111111
59ItOp111111111111111111111
59IpOt111111111111111111111
61IpOp111111111111111111111

CONTINUED IN NEXT SEGMENT

APPENDIX TO CHAPTER 53 – THIRD SEGMENT – FACTORS F43-F63.

NF = Number of Factors.

NF

FORMULAS

F43F44F45F46F47F48F49F50F51F52F53F54F55F56F57F58F59F60F61F62F63
Elements:
1An000000000000000000000
1En000000000000000000000
3Ac000000000000000000000
3Ec000000000000000000000
7A000000000000000000000
7E000000000000000000000
15At000000000100000000000
15Et000000000010000000000
31Ap000001010101010000100
31Ep000000101010110000010
32In111111010101001111101
32On111110101010101111011
48Ic111111111101111111111
48Oc111111111011111111111
56I111111111111111111111
56O111111111111111111111
60It111111111111111111111
60Ot111111111111111111111
62Ip111111111111111111111
62Op111111111111111111111
Compounds:
1AcInOp000000000000000000000
1AcEp000000000000000000000
1AIcEpOt000000000000000000000
1AEt000000000000000000000
1AtIEtO000000000000000000000
1AtE000000000000000000000
1ApItEOc000000000000000000000
1ApEc000000000000000000000
1IpEcOn000000000000000000000
2AcIn000000000000000000000
2AcOp000000000000000000000
2AInOt000000000000000000000
2AIcEp000000000000000000000
2AEpOt000000000000000000000
2AtIcEpO000000000000000000000
2AtIEt000000000000000000000
2AtEtO000000000000000000000
2ApIEtOc000000000000000000000
2ApItE000000000000000000000
2ApEOc000000000000000000000
2ItEOn000000000000000000000
2IpEc000000000000000000000
2EcOn000000000000000000000
3AInOp000000000000000000000
3AIcOt000000000000000000000
3AEp000000000000000000000
3AtIcEpOt000000000000000000000
3AtIEpO000000000000000000000
3AtEt000000000000000000000
3ApIEtO000000000000000000000
3ApItEtOc000000000000000000000
3ApE000000000000000000000
3ItEOc000000000000000000000
3IpEOn000000000000000000000
4AIn000000000000000000000
4AOt000000000000000000000
4AtInO000000000100000000000
4AtIcEp000000000000000000000
4AtEpO000000000000000000000
4ApIcEpOc000000000000010000000
4ApIEt000000000000000000000
4ApEtOc000000000000000000000
4IEtOn000000000010000000000
4ItE000000000000000000000
4EOn000000000000000000000
5AIcOp000000000000000000000
5AtIEpOt000000000000000000000
5ApItEtO000000000000000000000
5IpEOc000000000000000000000
6AIc000000000000000000000
6AOp000000000000000000000
6AtInOt000000000100000000000
6AtIcO000000000100000000000
6AtIEp000000000000000000000
6AtEpOt000000000000000000000
6ApIcEpO000000000000010000000
6ApIEpOc000000000000010000000
6ApItEt000000000000000000000
6ApEtO000000000000000000000
6IEtOc000000000010000000000
6ItEtOn000000000010000000000
6IpE000000000000000000000
6EOc000000000000000000000
7AtInOp000000000100000000000
7AtIO000000000100000000000
7AtEp000000000000000000000
7ApIcEpOt000000000000010000000
7ApItEpOc000000000000010000000
7ApEt000000000000000000000
7IEtO000000000010000000000
7IpEtOn000000000010000000000
8AtIn000000000100000000000
8AtO000000000100000000000
8ApInOc000001010001000000100
8ApIcEp000000000000010000000
8ApEpOc000000000000010000000
8IcEpOn000000101000100000010
8IEt000000000010000000000
8EtOn000000000010000000000
9AtIcOt000000000100000000000
9ApIEpO000000000000010000000
9ItEtOc000000000010000000000
11AtIcOp000000000100000000000
11AtIOt000000000100000000000
11ApIEpOt000000000000010000000
11ApItEpO000000000000010000000
11ItEtO000000000010000000000
11IpEtOc000000000010000000000
12AtIc000000000100000000000
12AtOt000000000100000000000
12ApInO000001010101000000100
12ApIcOc000001010001010000100
12ApIEp000000000000010000000
12ApEpO000000000000010000000
12IcEpOc000000101000110000010
12IEpOn000000101010100000010
12ItEt000000000010000000000
12EtOc000000000010000000000
13AtIOp000000000100000000000
13ApItEpOt000000000000010000000
13IpEtO000000000010000000000
14AtI000000000100000000000
14AtOp000000000100000000000
14ApInOt000001010101000000100
14ApIOc000001010001010000100
14ApItEp000000000000010000000
14ApEpOt000000000000010000000
14IcEpO000000101000110000010
14ItEpOn000000101010100000010
14IpEt000000000010000000000
14EtO000000000010000000000
15ApInOp000001010101000000100
15ApItOc000001010001010000100
15ApEp000000000000010000000
15IcEpOt000000101000110000010
15IpEpOn000000101010100000010
16ApIn000001010101000000100
16ApOc000001010001010000100
16InOn111110000000001111001
16IcEp000000101000110000010
16EpOn000000101010100000010
18ApIcO000001010101010000100
18IEpOc000000101010110000010
21ApIcOt000001010101010000100
21ApIO000001010101010000100
21IEpO000000101010110000010
21ItEpOc000000101010110000010
23ApIcOp000001010101010000100
23ApItO000001010101010000100
23IEpOt000000101010110000010
23IpEpOc000000101010110000010
24ApIc000001010101010000100
24ApO000001010101010000100
24InOc111111010001001111101
24IcOn111110101000101111011
24IEp000000101010110000010
24EpOc000000101010110000010
25ApIOt000001010101010000100
25ItEpO000000101010110000010
27ApIOp000001010101010000100
27ApItOt000001010101010000100
27ItEpOt000000101010110000010
27IpEpO000000101010110000010
28ApI000001010101010000100
28ApOt000001010101010000100
28InO111111010101001111101
28IOn111110101010101111011
28ItEp000000101010110000010
28EpO000000101010110000010
29ApItOp000001010101010000100
29IpEpOt000000101010110000010
30ApIt000001010101010000100
30ApOp000001010101010000100
30InOt111111010101001111101
30ItOn111110101010101111011
30IpEp000000101010110000010
30EpOt000000101010110000010
31InOp111111010101001111101
31IpOn111110101010101111011
36IcOc111111111001111111111
42IcO111111111101111111111
42IOc111111111011111111111
45IcOt111111111101111111111
45ItOc111111111011111111111
47IcOp111111111101111111111
47IpOc111111111011111111111
49IO111111111111111111111
53IOt111111111111111111111
53ItO111111111111111111111
55IOp111111111111111111111
55IpO111111111111111111111
57ItOt111111111111111111111
59ItOp111111111111111111111
59IpOt111111111111111111111
61IpOp111111111111111111111

END OF TABLE

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2016-08-05T05:57:18+00:00